Keywords and Synonyms
Static membership ; Approximate membership
Problem Definition
The Problem and the Model
A static data structure problem consists of a set of data D, a set of queries Q, a set of answers A, and a function \( { f \colon D \times Q \rightarrow A } \). The goal is to store the data succinctly so that any query can be answered with only a few probes to the data structure. Static membership is a well-studied problem in data structure design [1,4,7,8,12,13,16].
Definition 1 (Static Membership)
In the static membership problem, one is given a subset S of at most n keys from a universe \( { U=\{1,2,\ldots,m\} } \). The task is to store S so that queries of the form “Is u in S?” can be answered by making few accesses to the memory.
A natural and general model for studying any data structure problem is the cell probe model proposed by Yao [16].
Definition 2 (Cell Probe Model)
An \( { (s,w,t) } \) cell probe scheme for a static data structure problem \( { f \colon D \times Q...
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Srinivasan, V. (2008). Approximate Dictionaries. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_16
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